Mr. Ward's Teaching Materials

GM Lesson 016 Goods and Services Tax

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GM Lesson 016: Goods and Services Tax

Learning Intentions

By the end of this lesson, students will be able to:

  • Calculate GST on goods and services.
  • Determine prices before and after GST.
  • Interpret GST calculations in consumer contexts.

Prerequisites

Students should already be able to:

  • Calculate of an amount.
  • Increase an amount by a percentage.
  • Divide by a decimal multiplier.
  • Interpret percentage mark-ups and discounts in financial contexts.
  • Round money values to the nearest cent.

Key Idea Summary

Goods and Services Tax, usually called GST, is a tax added to many goods and services.

In this lesson, GST is calculated at .

If a price does not include GST, then:

The GST-inclusive price is:

Equivalently:

If a price already includes GST, then:

The GST amount inside a GST-inclusive price can also be found using:

This works because the GST-inclusive price contains equal parts: parts for the original price and part for GST.

Direct Instruction and Worked Examples

Lesson Timing

Time Allocation

Time Allocation

  • Introduction, warmup and vocabulary: 5 minutes
  • Direct instruction: 15 minutes
  • Understanding checks: 5 minutes
  • Exercises: 20 minutes
  • Homework: 20 to 30 minutes outside the lesson it was taught in.
Link to original

Direct Instruction

A price may be described in two different ways:

  • GST-exclusive price: GST has not yet been added.
  • GST-inclusive price: GST has already been added.

For a GST-exclusive price, GST is added as a increase.

That means:

So adding GST is the same as multiplying by:

To reverse GST, divide by:

Worked Example 1: Calculating GST on a Service

A plumber charges $ before GST. Calculate the GST and the total price including GST.

The GST is:

So the GST is $ .

The total price including GST is:

Therefore, the GST-inclusive price is $ .

Worked Example 2: Finding a GST-Inclusive Price Directly

A desk has a GST-exclusive price of $ . Find the GST-inclusive price.

Since GST increases the price by :

Therefore, the GST-inclusive price is $ .

Worked Example 3: Finding the Price Before GST

A laptop bag costs $ including GST. Find the price before GST.

Since:

we reverse this by dividing by :

Therefore, the price before GST is $ .

Worked Example 4: Finding the GST Included in a Price

A restaurant bill is $ including GST. Find the GST included in the bill.

For a GST-inclusive price:

Therefore, the GST included is $ .

The price before GST is:

So the bill is made up of $ before GST and $ GST.

Worked Example 5: Interpreting GST in a Receipt

A receipt shows the following information:

ItemGST-exclusive price
Headphones$
Phone case$
Charging cable$

Find the subtotal before GST, the GST and the total price including GST.

First find the subtotal before GST:

So the subtotal before GST is $ .

Now calculate GST:

So the GST is $ .

Now calculate the GST-inclusive total:

Therefore, the total price including GST is $ .

Understanding Checks

Check 1

A bicycle repair costs $ before GST.

  1. What is of $ ?
  2. What is the GST?
  3. What is the total price including GST?

Check 2

A chair costs $ including GST.

  1. Should you multiply by or divide by to find the price before GST?
  2. Find the price before GST.
  3. Find the GST included in the price.

Check 3

Decide whether each statement is true or false.

  1. Adding GST means increasing the original price by .
  2. A GST-inclusive price is always smaller than the price before GST.
  3. To remove GST from a GST-inclusive price, divide by .
  4. The GST included in a GST-inclusive price is of the GST-inclusive price.

Check 4

A price before GST is $ .

Explain why the GST-inclusive price is not found by adding $ .

Exercises

Simple Familiar Exercises

Exercise 1

Calculate the GST on each GST-exclusive price.

  1. $
  2. $
  3. $
  4. $
  5. $

Exercise 2

Calculate the GST-inclusive price for each GST-exclusive price.

  1. $
  2. $
  3. $
  4. $
  5. $

Exercise 3

For each GST-inclusive price, calculate the price before GST.

  1. $
  2. $
  3. $
  4. $
  5. $

Exercise 4

For each GST-inclusive price, calculate the GST included.

  1. $
  2. $
  3. $
  4. $
  5. $

Complex Familiar Exercises

Exercise 5

A mechanic charges the following GST-exclusive amounts:

ItemPrice before GST
Labour$
Parts$
Disposal fee$

Calculate:

  1. the subtotal before GST
  2. the GST
  3. the total price including GST

Exercise 6

A computer store advertises a monitor for $ including GST.

Calculate:

  1. the price before GST
  2. the GST included
  3. the nearest whole-dollar estimate of the GST

Exercise 7

A gardener charges $ per hour before GST and works for hours.

Calculate:

  1. the total charge before GST
  2. the GST
  3. the total charge including GST

Exercise 8

A business buys identical notebooks for $ each before GST.

Calculate:

  1. the total price before GST
  2. the GST
  3. the total price including GST

Exercise 9

A GST-inclusive invoice total is $ . The GST included is to be reported separately.

Calculate:

  1. the GST included
  2. the price before GST
  3. check that adding GST to the price before GST gives the original invoice total

Homework Problems

Homework 1

Calculate the GST and GST-inclusive price for each GST-exclusive amount.

  1. $
  2. $
  3. $
  4. $

Homework 2

Calculate the price before GST and the GST included for each GST-inclusive amount.

  1. $
  2. $
  3. $
  4. $

Homework 3

A bicycle shop sells a helmet for $ before GST and a lock for $ before GST.

Calculate:

  1. the total price before GST
  2. the GST
  3. the total price including GST

Homework 4

A tradesperson sends an invoice for $ including GST.

Calculate:

  1. the price before GST
  2. the GST included
  3. a sentence explaining what the GST amount represents

Homework 5

A GST-exclusive price is increased by GST to become $ .

Find the original GST-exclusive price and the GST amount.

Next: GM Lesson 017 Simple Interest

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